nLab world sheets for world sheets




A mechanism in the context of string theory:

before gauge fixing, the worldsheet QFT describing the first-quantized string (see also at What is a particle? for conceptual background is a 2d quantum gravity coupled to scalar fields (the embedding fields that say how the string sits in target spacetime). Being quantum gravity, even if in the comparatively extremely simple case of only two dimensions, one may ask if this arises as the effective field theory/second quantization of another kind of string, one whose target spacetime is the worldsheet of the original string.

This idea is known as “world sheets for world sheets”, going back to (Green87).

This may be compared to how the worldvolume theory of the topological membrane which is a Chern-Simons theory, arises as the second quantization of topological strings (A-model) for which that 3d worldvolume of the membrane is their target space (Witten 92), see at TCFT – Worldsheet and effective background theories for more on this.


  • Michael Green, World Sheets for World Sheets, Nucl.Phys. B293 (1987) 593-611

    Abstract In this paper I suggest that the two-dimensional world sheet underlying the dynamics of relativistic strings may itself emerge from an approximation to a two-dimensional string theory. Coordinates that represent space-time and internal symmetries should emerge as wave functions of the massless states of that theory. This is motivated by studying various string theories with two-dimensional target spaces and internal symmetry which are related to generalized nonlinear sigma models.

See also

  • Eliezer Rabinovici, World sheets for world sheets revisited (talk, slides)

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